Wealth Effect on Portfolio Allocation in Incomplete Markets
76 Pages Posted: 22 Apr 2020 Last revised: 19 Mar 2024
Date Written: March 10, 2024
Abstract
In this paper, we develop a novel decomposition of optimal dynamic portfolio choice under flexible incomplete market models and the wealth-dependent HARA utility. The decomposition reveals the fundamental impacts from market incompleteness and wealth effect in portfolio allocation. With hedgeable interest rate risk, the optimal portfolio under HARA utility can be decomposed to a pure CRRA optimal portfolio and a financing portfolio for the investor’s future subsistence requirements. In this case, the wealth growth rate is always higher for HARA investors with higher initial wealth levels, leading to increased wealth inequality. As an application of our decomposition, we solve the HARA optimal policy in closed-form under an incomplete market model with both stochastic interest rate and volatility. Using parameters calibrated from U.S. market data, we find that the wealth effect generates a procyclical pattern in investor’s stock positions and time varying risk aversion levels in different market regimes. Moreover, we identify a novel “buy-high-sell low” effect that may hurt the HARA investors with low initial wealth.
Keywords: optimal portfolio choice, incomplete market, wealth-dependent utility, closed-form analysis, wealth inequality, heterogenous investors.
JEL Classification: C61, C63, G11
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